Simulation of single mode Richtmyer-Meshkov instability using the adaptive free Lagrange method

Because of extreme deformation, instability problems have been traditionally modeled using Eulerian techniques or Arbitrary Lagrange Euler (ALE) techniques. The free-Lagrange (FL) method first introduced by Crowley offers a third basic alternative. The specific FL method described in this paper consists of: (1) a 2D staggered-grid hydrodynamics (SGH) differencing scheme appropriate to an unstructured mesh consisting of triangular and quadrilateral zones; (2) a set of primitive mesh optimization algorithms; and (3) a set of rules for adaptive mesh refinement which we refer to as the adaptive free Lagrange (AFL) method. In a previous study, Burton showed that the spurious vorticity commonly associated with SGH differencing results from a failure to explicity conserve angular momentum in the difference equations. This led to a significantly improved technique for removing the spurious vorticity, called spurious vorticity damping (SVD). SVD was shown to produce superior results in a test problem which had no intrinsic vorticity. In the present study, SVD is shown to also produce superior results in a problem with intrinsic vorticity. The AFL and SVD methods are applied to a low Mach number shock tube problem and compared with other methods. AFL seems to perform as well as Eulerian methods and ismore » somewhat better at resolving fine structures in the calculation. The SVD method produced results far superior to other methods tried. 21 refs., 10 figs.« less